A country may default on its government debt (in any sense, e.g. miss a payment) within the next year. How would one estimate the expected (under the risk-neutral measure) currency depreciation by year end conditional on the sovereign default within one year? Rigorously put, I am interested in:

$$E_t^Q \left[ S_T/S_t|\tau_{d} < T \right],$$

where $S$ is the spot exchange rate, $T$ is a fixed time horizon, say, 1 year, and $\tau_d \in (t, T)$ is the time of default.

One way would be to use the quanto CDS vs. local-currency CDS rates. Let us assume it is not feasible as local-currency CDS are not traded.

Another way would be to estimate the historical average depreciation on the subset of countries that have ever defaulted and pretend that this is under $Q$.

$\begingroup$@AK88 only the marginal distribution thereof, with the default/no default probability factored in. I need to integrate it out somehow.$\endgroup$
– Igor PozdeevAug 29 '19 at 6:11

$\begingroup$For countries in the eu you can look at something called quanto cds - you can look at the difference between cds in euros and cds in usd, which allows you to get an impression of the impact a default event has on the currency.$\endgroup$
– willSep 8 '19 at 19:29

2 Answers
2

I have actually looked into this a lot and I don't have a full answer.

You can (sort of) see what the market participants think by looking at the consensus "quanto factors" published monthly by IHS Markit Totem. They even have some term structure, although usually it's the same factor for all tenors. For some sovereigns, people sometimes trade a CDS denominated in local currency referencing hard-currency debt. (This stuff isn't novel, by the way - LTCM used to trade quanto CDS on the likes of Italy back in the 1990s.) The idea is that if the sovereign defaults, then the protection buyer gets paid the notional using the post-default exchange rate. So the CDS spread (market standard quote) is discounted in comparison with the USD-denominated CDS spread by the quanto factor, which is approximately 1-the devaluation on default. (Totem also has quanto factors for many names denominated in EUR and JPY.)

(As an aside, there are other kinds of contracts you could use to express a view on the quanto factor, which you could then hedge with the more vanilla quanto CDS. For example (self-referencing extinguisher) you loan to a credit-risky foreign sovereign their own local currency, with a clause that the loan is torn up (extinguishes) if the sovereign defaults on hard-currency bonds. Or (extinguishing cross-currency swap) you could pay USD to a corporation in another country and receive local currency, again with a clause that if their soveregn defaults on hard-currency bonds, then you extinguish either the local-currency leg or both legs.)

But how meaningful are the consensus quanto factors? It is available for only a few countries. There are usually much fewer than 10 contributors, and they don't actually trade often, just mark their books. I would not be surprised if the quanto factor turns out to be far from the consensus number when a trade actually happens, and even further from reality when a sovereign default actually happens.

You can also try getting indicative quanto factors from inter-dealer brokers like TP ICAP and BGC Fenics MD, with similar caveats.

You could look at the history of sovereign defaults, such as Moody's, S&P, or Bank of Canada CRAG, and try to figure the FX depreciations (noting that some depreciation happens before the default), and take some kind of average. I am skeptical that this would be meaningful, given that every default is very different, and there are so few of them.

You could collect fundamental data like GDP growth, local equities, inflation, and FX forwards, and build some kind of econometric structural model-like calculation. I've seen a few attempts at doing this and was not impressed. (Such models can be used to saisfy a product control group that the quanto factor marked by traders is not entirely made up.)

As an extercise in machine learning, you could collect as much country econometric data as you could find, and country news, correlate it to the historical databases of sovereign defaults and to the quanto factors from Totem, and then you may be able to predict

what the Totem consensus quanto factor would be for a country that's not in Totem

how Totem consensus quanto factor will react to the newly available economic data and news.

Similar to above, I’ve wargamed this one in the past and come to the the simple conclusion that the currency and local equity return are informative about the probability of default.

Defaults are not typically informative about currency risk, because the currency typically jumps (on the USDCCY basis in EM) in the “crisis”, well before any default actually does or does not follow.

My natural bias would be to assume that the Grainger Causality flows the other way. Currencies predict defaults more than defaults move currencies.

That said, sometimes bosses just need answering, even if their question is wrong :-) in which case, just go Bayesian on his ****. Calculate the p(default|FX) with logistic regression, multiply by p(FX) (given by the IV and realised move), and divide by p(default) = p(default|FX) * p(Fx) + p(no-default|FX) * p(FX). Then you have p[FX|default).